We investigate questions related to the time evolution of discrete graph dynamical systems where each node has a state from {0,1}. The configuration of a system at any time instant is a Boolean vector that specifies the state of each node at that instant. We say that two configurations are similar if the Hamming distance between them is small. Also, a predecessor of a configuration B is a configuration A such that B can be reached in one step from A. We study problems related to the similarity of predecessor configurations from which two similar configurations can be reached in one time step. We address these problems both analytically and experimentally. Our analytical results point out that the level of similarity between predecessors of two similar configurations depends on the local functions of the dynamical system. Our experimental results, which consider random graphs as well as small world networks, rely on the fact that the problem of finding predecessors can be reduced to the Boolean Satisfiability problem (SAT).
Testing phase space properties of synchronous dynamical systems with nested canalyzing local functions.
Discrete graphical dynamical systems serve as effective formal models in many contexts, including simulations of agentbased models, propagation of contagions in social networks and study of biological phenomena. A class of Boolean functions, called nested canalyzing functions (NCFs), has been used as a good model of certain biological phenomena. Motivated by these biological applications, we study a variety of analysis problems for synchronous graphical dynamical systems (SyDSs) over the Boolean domain, where each local function is an NCF. Each analysis problem involves testing whether the phase space of a given SyDS satisfies a certain property. We present intractability results for some properties as well as efficient algorithms for others. In several cases, our results clearly delineate intractable and efficiently solvable versions of problems
 Award ID(s):
 1633028
 Publication Date:
 NSFPAR ID:
 10067760
 Journal Name:
 AAMAS 2018
 Page Range or eLocationID:
 15851594
 Sponsoring Org:
 National Science Foundation
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